12,431 research outputs found
Branching processes, the max-plus algebra and network calculus
Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory
Noise Correlations in one-dimensional systems of ultra-cold fermions
Time of flight images reflect the momentum distribution of the atoms in the
trap, but the spatial noise in the image holds information on more subtle
correlations. Using Bosonization, we study such noise correlations in generic
one dimensional systems of ultra cold fermions. Specifically, we show how
pairing as well as spin and charge density wave correlations may be identified
and extracted from the time of flight images. These incipient orders manifest
themselves as power law singularities in the noise correlations, that depend on
the Luttinger parameters, which suggests a general experimental technique to
obtain them.Comment: 5 pages, 3 figures. Added discussion on the visibility of noise
correlation features for realistic condition
Decay of superfluid currents in a moving system of strongly interacting bosons
We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.Accepted manuscrip
Evolution of the Fermi surface in phase fluctuating d-wave superconductors
One of the most puzzling aspects of the high superconductors is the
appearance of Fermi arcs in the normal state of the underdoped cuprate
materials. These are loci of low energy excitations covering part of the fermi
surface, that suddenly appear above instead of the nodal quasiparticles.
Based on a semiclassical theory, we argue that partial Fermi surfaces arise
naturally in a d-wave superconductor that is destroyed by thermal phase
fluctuations. Specifically, we show that the electron spectral function
develops a square root singularity at low frequencies for wave-vectors
positioned on the bare Fermi surface. We predict a temperature dependence of
the arc length that can partially account for results of recent angle resolved
photo emission (ARPES) experiments.Comment: Journal ref. adde
Decay of super-currents in condensates in optical lattices
In this paper we discuss decay of superfluid currents in boson lattice
systems due to quantum tunneling and thermal activation mechanisms. We derive
asymptotic expressions for the decay rate near the critical current in two
regimes, deep in the superfluid phase and close to the superfluid-Mott
insulator transition. The broadening of the transition at the critical current
due to these decay mechanisms is more pronounced at lower dimensions. We also
find that the crossover temperature below which quantum decay dominates is
experimentally accessible in most cases. Finally, we discuss the dynamics of
the current decay and point out the difference between low and high currents.Comment: Contribution to the special issue of Journal of Superconductivity in
honor of Michael Tinkham's 75th birthda
Dynamical instability of a spin spiral in an interacting Fermi gas as a probe of the Stoner transition
We propose an experiment to probe ferromagnetic phenomena in an ultracold
Fermi gas, while alleviating the sensitivity to three-body loss and competing
many-body instabilities. The system is initialized in a small pitch spin
spiral, which becomes unstable in the presence of repulsive interactions. To
linear order the exponentially growing collective modes exhibit critical
slowing down close to the Stoner transition point. Also, to this order, the
dynamics are identical on the paramagnetic and ferromagnetic sides of the
transition. However, we show that scattering off the exponentially growing
modes qualitatively alters the collective mode structure. The critical slowing
down is eliminated and in its place a new unstable branch develops at large
wave vectors. Furthermore, long-wavelength instabilities are quenched on the
paramagnetic side of the transition. We study the experimental observation of
the instabilities, specifically addressing the trapping geometry and how
phase-contrast imaging will reveal the emerging domain structure. These probes
of the dynamical phenomena could allow experiments to detect the transition
point and distinguish between the paramagnetic and ferromagnetic regimes
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